Lesson 4: Practice Problems

Problem 1

Select all of the parallelograms. For each figure that is not selected, explain how you know it is not a parallelogram.

  1. A blue trapezoid on a blank grid with one base of 5, the other base is 3, and a height of 2.
  2. A blue parallelogram on a grid measuring 2x5
  3. A blue rectangle on a grid measuring 3x4
  4. A blue irregular shape on a grid with a height of 3 and width of 3.
  5. A blue right triangle on a grid with a height of 4 and a base of 3

Problem 2

  1. Decompose and rearrange this parallelogram to make a rectangle.

    A blue parallelogram on a blank grid with a height of 5 and a width of 9

  2. What is the area of the parallelogram? Explain your reasoning.

Problem 3

Find the area of the parallelogram.

A parallelogram with one side labeled 3.2 centimeters, and another side labeled 10 centimeters. A dashed line perpendicular to the 10 centimeter sides is labeled 3 centimeters

Problem 4

Explain why this quadrilateral is not a parallelogram.

A quadrilateral with a bottom side length of 8 units, a top side length of 4 units. The left side ascends 5 units while moving right 13 units, and the right side ascends 5 units while moving right 9 units.

Problem 5 From Unit 1 Lesson 3

Find the area of each shape. Show your reasoning.

  1. A shape with eight sides. Four sides are straight sides and extend left, right, up and, down for 2 units each. The remaining sides are angled sides connecting each of the straight sides to the next. The shape is a total of 6 units tall and 6 units wide.
  2. A shape with six sides. It is 9 units long and six units wide at it’s widest point. Two vertical sides connect four sloped sides, which meet at either end of the shape.

Problem 6 From Unit 1 Lesson 1

Find the areas of the rectangles with the following side lengths.

  1. 5 in and in

  2. 5 in and in

  3. in and in

  4. in and in